CN106373082A - Cellular automata and chaotic mapping-based digital image encryption method and decryption method thereof - Google Patents

Abstract

The invention provides a cellular automata and chaotic mapping-based digital image encryption method and a decryption method thereof. The encryption method includes the following steps that: a 288-bit key is utilized to generate chaotic mapping parameters and cellular automaton evolution rules which are required by an encryption algorithm; pre-processing such as three-dimensional decomposition and blocking, is carried out on an original image; 3D chaotic mapping is adopted to scramble pixel positions; cross-exclusive-OR operation is performed on image blocks to be encrypted; and a 2D second-order cellular automata used for generating boundaries, which is provided by the present invention, is utilized to carry out iterative encryption on an unfolded plaintext, pixels are mixed, and iteration is repeated until an iteration requirement is satisfied; and reverse pre-processing is carried out, and blocked ciphertext images are combined into a ciphertext image.

Description

Digital image encryption and decryption method based on cellular automaton and chaotic mapping

Technical Field

The invention relates to the field of digital image processing, in particular to a digital image encryption and decryption method based on cellular automata and chaotic mapping.

Background

The digital image represents information by visual effect, the data volume is large, the correlation between pixels is high, the requirement of real-time encryption is high, and the classic cryptography method cannot well meet the requirement. Therefore, the technology for digital image encryption attracts a wide attention of scholars and is gradually becoming an important branch in cryptography.

Digital image encryption is different from traditional data encryption, and mainly has the following characteristics: (1) the digital image represents information by a visual picture, so that the digital image has larger information quantity compared with the text information, and therefore, a long time is needed for encrypting the digital image by using a classical encryption algorithm, and the encryption efficiency is not high. (2) Digital images are stored in a two-dimensional matrix data format, and most algorithms cannot utilize the characteristic to carry out parallelization processing but carry out operations such as preprocessing, rearrangement and the like when the digital images are encrypted, so that the time is greatly increased, and the encryption efficiency is reduced. (3) Unlike information such as text, images allow some degree of distortion in encryption and decryption due to their visual characteristics. (4) The digital image has great correlation between adjacent pixels, and the representation shows that the values of the adjacent pixels are mostly similar or identical, and the correlation must be removed from the encrypted image, which means that the encryption algorithm has great sensitivity and higher requirements on security.

There are many existing digital image encryption schemes, which can be roughly divided into three directions, namely scrambling and substitution, so as to combine the two directions. Scrambling, also known as pixel scrambling, is performed by scrambling the positions of the pixels of the original image to achieve the purpose of encrypting the image. The main scrambling algorithms include Arnold mapping, Baker mapping, Magic mapping and the like, and derived scrambling algorithms thereof, and in recent years, chaotic systems are gradually becoming the trend of scrambling technology. Replacement means that the pixel value itself is replaced and changed. The image pixel values are replaced so that the histogram of the whole image is uniformly distributed and the correlation among pixels is reduced as much as possible. The replacement of pixels by the evolution of cellular automata has become a trend in recent years.

At present, because the scrambling operation of each time is very simple, the traditional scrambling algorithms such as Arnold mapping, Baker mapping, Magic mapping and the like can achieve ideal scrambling effect after a plurality of scrambling operations; secondly, as the scrambling operation does not change the value of each pixel, the statistical characteristics of the pixels are not changed, which brings great potential safety hazard; the scheme of encrypting the digital image by using chaotic mapping has the advantages that most of keys are short, and the scheme has great potential safety hazard when violent cracking is faced; in addition, the chaos mapping is singly used as an encryption means, the relative confusion degree is not high enough, and the chaos mapping is easy to break when a plaintext attack is selected; the scheme of digital image encryption by using the cellular automata has the advantages of high requirement on most iteration times, more encryption rounds, low encryption efficiency and incapability of meeting the real-time property.

Disclosure of Invention

The invention provides a digital image encryption method based on a cellular automaton and chaotic mapping, which has good encryption effect and better chaotic characteristic.

Still another object of the present invention is to provide a decryption method of the digital image encryption method based on the cellular automata and the chaotic map.

In order to achieve the technical effects, the technical scheme of the invention is as follows:

a digital image encryption method based on cellular automata and chaotic mapping comprises the following steps:

s1: generating a key to generate a coefficient, iteration times and an evolution rule of a cellular automaton of the 3D chaotic mapping;

s2: preprocessing an image to be encrypted;

s3: pixel position scrambling is carried out on the pixels of the preprocessed image by using the coefficient of the 3D chaotic mapping obtained in the S1;

s4: and (4) carrying out iterative encryption on the plaintext block of the image after the pixel scrambling by using the cellular automata evolution rule obtained in the S1, repeating iteration until the iteration requirement is met, and finally carrying out reverse preprocessing to obtain the ciphertext image.

Further, the specific process of step S1 is as follows:

selecting a 288-bit binary bit stream as a key to generate the coefficients of the 3D chaotic mapping, the iteration times and the rule numbers of the evolution rules of the cellular automata, wherein the key generation algorithm is that the first 7 × 32 bits represent an integer for each 32 bits, and the integers are respectively used as six coefficients of the 3D chaotic mapping (a)_xa_ya_zb_xb_yb_z) And the iteration number t, and the last 64 bits form the rule number r of the cellular automaton.

Further, the specific process of step S2 is as follows:

the pixels of the gray-scale image to be encrypted, which are plain text, are rendered three-dimensional, with the length and height of the image M being W and H, respectively, and the decomposition can be performed according to the following equation:

$W\×H=2N_1^3+2N_2^3+\mathrm{...}+2N_k^3+R---\left(1\right)$

wherein,representing two pixel cubes of equal size, each of length N_kR ∈ (0,1,2, …, 15) is a tail item that cannot be decomposed and is ignored in the subsequent encryption process.

Further, the specific process of step S3 is as follows:

s31: establishing a 3D chaotic mapping function:

2) the conventional Arnold transform is transformed by introducing two parameters a and b:

$\left(\begin{array}{c}{x}_{i+1}\\ y_{i+1}\end{array}\right)=\left(\begin{array}{cc}1& 1\\ 1& 2\end{array}\right)\left(\begin{array}{c}{x}_i\\ y_i\end{array}\right)\left(\mathrm{mod}p\right)---\left(3\right)$

expanding to equation (4):

$\left(\begin{array}{c}{x}_{i+1}\\ y_{i+1}\end{array}\right)=\left(\begin{array}{cc}1& a\\ b& ab+1\end{array}\right)\left(\begin{array}{c}{x}_i\\ y_i\end{array}\right)\left(\mathrm{mod}p\right)---\left(4\right)$

2) keeping z unchanged, and performing two-dimensional Arnold transformation on the formula (4) in an x-y plane to obtain a formula (5):

$\left(\begin{array}{c}{x}_{i+1}\\ y_{i+1}\\ z_{i+1}\end{array}\right)=\left(\begin{array}{ccc}1& a_z& 0\\ b_z& a_z{b}_z+1& 0\\ 0& 0& 1\end{array}\right)\left(\begin{array}{c}{x}_i\\ y_i\\ z_i\end{array}\right)\left(\mathrm{mod}1\right)---\left(5\right)$

3) keeping x unchanged, and performing two-dimensional Arnold transformation on the formula (4) in a y-z plane to obtain a formula (6):

$\left(\begin{array}{c}{x}_{i+1}\\ y_{i+1}\\ z_{i+1}\end{array}\right)=\left(\begin{array}{ccc}1& 0& 0\\ 0& 1& a_x\\ 0& b_x& a_x{b}_x+1\end{array}\right)\left(\begin{array}{c}{x}_i\\ y_i\\ z_i\end{array}\right)\left(\mathrm{mod}1\right)---\left(6\right)$

4) keeping y unchanged, and performing two-dimensional Arnold transformation on the formula (4) in an x-z plane to obtain a formula (7):

$\left(\begin{array}{c}{x}_{i+1}\\ y_{i+1}\\ z_{i+1}\end{array}\right)=\left(\begin{array}{ccc}1& 0& a_y\\ 0& 1& 0\\ b_y& 0& a_y{b}_y+1\end{array}\right)\left(\begin{array}{c}{x}_i\\ y_i\\ z_i\end{array}\right)\left(\mathrm{mod}1\right)---\left(7\right)$

5) multiplying the coefficient matrixes in the formulas (5), (6) and (7) to obtain a 3D chaotic mapping formula (8):

$\left(\begin{array}{c}{x}_{i+1}\\ y_{i+1}\\ z_{i+1}\end{array}\right)=A\left(\begin{array}{c}{x}_i\\ y_i\\ z_i\end{array}\right)\left(\mathrm{mod}p\right)---\left(8\right)$

wherein,

$A=\left(\begin{array}{ccc}1+a_x{a}_z{a}_y& a_z& a_y+a_x{a}_z+a_x{a}_y{a}_z{b}_x\\ b_z+a_x{b}_y+a_x{a}_z{b}_y{b}_z& a_z{b}_z+1& a_y{a}_z+a_x{a}_y{a}_z{b}_y{b}_z+a_x{a}_z{b}_z+a_x{a}_y{b}_y+a_x\\ a_x{b}_x{b}_y+b_y& b_x& a_x{a}_y{b}_x{b}_y+a_x{b}_x+a_y{b}_y+1\end{array}\right),$

a_xa_ya_zb_xb_yb_zall are positive integers, N is the length of the cube, i ∈ [0, N-1]X, y and z are coordinates of a pixel in a three-dimensional space respectively;

s32: and performing position scrambling processing on the pixels by using the obtained 3D chaotic mapping function:

firstly, carrying out 3D chaotic mapping on Q once by using a formula (2) to obtain Q₁Then Q is₁And Q' is exclusive-OR (XOR) at each position to obtain QThen to Q'₁Performing 3D chaotic mapping to obtain Q'₂And finally Q₁And Q'₂Performing an exclusive OR (XOR) operation to obtain Q₂I.e. byWhere Q and Q' characterize a pair of pixel cubes of equal volume for the image.

Further, the specific process of step S4 is as follows:

handle Q₂And Q'₂Expanding into two-dimensional plane according to position, and respectively using the two-dimensional plane as two initial states C of 2D second-order cellular automata evolution₀And C₁Calculating C₀And C₁The Hash value is used as an initial value and a parameter of piecewise linear chaotic mapping so as to generate a random boundary of the cellular automaton, and a global evolution function is obtained according to a rule number rG is C_t+1＝G(C_t,C_t-1) And carrying out two evolutions on the two initial states by using the same to obtain C₂And C₃Mixing C with₂And C₃Reconstructing a pixel cube, taking the cube as a primary encryption iteration, judging whether the iteration number reaches t times, if so, reversely constructing an encrypted image according to a formula (1): otherwise, go to step S3 to perform the next iteration until the number of times is satisfied.

A decryption method of a digital image encryption method based on a cellular automaton and chaotic mapping comprises the following steps:

s61: generating parameters of 3D chaotic mapping and rule numbers of a 2D second-order cellular automaton by using the 288-bit binary stream key which is the same as that in the encryption stage in the same way;

s62: preprocessing the image to be decrypted in the same way as the encryption stage;

s63: performing reverse iteration of the cellular automaton on the pixel blocks, and setting two initial states of the cellular automaton formed by the ciphertext image blocks as C₂And C₃Respectively calculating the Hash values of the two, thereby generating a random boundary of the cellular automata, and obtaining a reverse global evolution function G' according to a rule number r because an inverse rule of the second-order cellular automata is the random boundary of the second-order cellular automata, so that C_t-1＝G′(C_t,C_t+1) After two evolutions, C is obtained₁And C₀；

S64: establishing an inverse mapping function of the 3D chaotic mapping:

$\left(\begin{array}{c}{x}_i\\ y_i\\ z_i\end{array}\right)=A^{-1}\left(\begin{array}{c}{x}_{i+1}\\ y_{i+1}\\ z_{i+1}\end{array}\right)\left(\mathrm{mod}N\right)$

wherein A is^-1Is the inverse matrix of A, N is the length of the cube, i ∈ [0, N-1]X, y and z are coordinates of a pixel in a three-dimensional space respectively, and the pixel blocks obtained by decryption in S63 are subjected to cross exclusive OR (XOR) operation and inverse operation of 3D chaotic mapping respectively;

s65: and (3) circularly executing the steps S63 and S64 until the iteration number t defined in the key is met, thereby completing the whole decryption process, and finally reconstructing the plaintext image according to the inverse operation of the formula (1) and completing the decryption.

Compared with the prior art, the technical scheme of the invention has the beneficial effects that:

compared with the traditional chaotic mapping, the 3D chaotic mapping adopted by the invention has better chaotic characteristics and can achieve the scrambling effect more quickly; the method is different from a cycle boundary or a mirror image boundary adopted by the traditional cellular automata, and provides a random generation boundary, so that the evolution of the cellular automata has chaotic characteristics, and the known plaintext attack and the selected plaintext attack can be resisted; 3D chaotic mapping and a cellular automaton are combined in a cross encryption iteration mode, so that the key space reaches 288 bits, brute force cracking attack can be effectively resisted, and the encryption effect is better; based on the idea of block encryption, the chaotic mapping and the evolution of the cellular automata can be parallel, so that the scheme has the capability of parallel processing; the method meets the requirement of security, is a lossless and non-expansive image encryption scheme, ensures the universality of the method in image encryption, and can be conveniently transplanted to the encryption of compressed images.

Drawings

FIG. 1 is a flow chart of an encryption method of the present invention;

FIG. 2 is a three-dimensional exploded view of a two-dimensional image during encryption in accordance with the present invention;

FIG. 3 is a diagram of the evolution stage of the cellular automata during the encryption process of the present invention;

FIG. 4 is a flow chart of the decryption method of the present invention;

FIG. 5 is a diagram of the reverse evolution stage of the cellular automata during the decryption process of the present invention.

Detailed Description

The drawings are for illustrative purposes only and are not to be construed as limiting the patent;

for the purpose of better illustrating the embodiments, certain features of the drawings may be omitted, enlarged or reduced, and do not represent the size of an actual product;

it will be understood by those skilled in the art that certain well-known structures in the drawings and descriptions thereof may be omitted.

The technical solution of the present invention is further described below with reference to the accompanying drawings and examples.

Example 1

As shown in fig. 1, a digital image encryption method based on cellular automata and chaotic mapping includes the following basic processes:

(1) a key generation phase;

(2) an image preprocessing stage;

(3) a pixel position scrambling stage;

(4) an evolution stage of the cellular automata;

(5) and (4) judging the iteration frequency condition according to the step (4) and outputting a result.

The following steps (1) to (5) are described in detail:

the step (1) comprises the following steps:

a key generation stage, selecting a binary bit stream with the length of 288 bits as a key to generate the coefficients and the iteration times of the 3D chaotic mapping and the rule number of the evolution rule of the cellular automata, wherein the key generation algorithm is that the first 7 × 32 bits represent an integer every 32 bits and are respectively used as six coefficients of the 3D chaotic mapping (a)_xa_ya_zb_xb_yb_z) And the iteration number t, and the last 64 bits form the rule number r of the cellular automaton.

The step (2) comprises the following steps:

the image pre-processing stage, the pixels of the grey-scale image as plain text are rendered three-dimensional (for a color RGB image it is possible to process each channel separately). Assuming that the length and height of the image M are W and H, respectively, the decomposition can be performed according to equation (1):

$W\×H=2N_1^3+2N_2^3+\mathrm{...}+2N_k^3+R---\left(1\right)$

wherein,representing two pixel cubes of equal size, each of length N_kR ∈ (0,1,2, …, 15) is a tail item that cannot be decomposed and is ignored in the subsequent encryption process, as shown in FIG. 2.

The step (3) comprises the following steps:

and a pixel position scrambling stage. Introducing a 3D chaotic mapping function according to the rule of the step (3-1), and discretizing the pixel position according to a formula (2) aiming at the pixel position which is a discretized positive integer:

$\left(\begin{array}{c}{x}_{i+1}\\ y_{i+1}\\ z_{i+1}\end{array}\right)=A\left(\begin{array}{c}{x}_i\\ y_i\\ z_i\end{array}\right)\left(\mathrm{mod}N\right)---\left(2\right)$

wherein N is the length of the cube, i belongs to [0, N-1], and x, y and z are the coordinates of a pixel in a three-dimensional space respectively.

Taking a pair of pixel cubes with equal volumes as an example, let Q and Q', firstly, Q is subjected to one-time 3D chaotic mapping by using a formula (2) to obtain Q₁Then Q is₁And Q' is exclusive-OR (XOR) at each position to obtain QThen to Q'₁Performing 3D chaotic mapping to obtain Q'₂And finally Q₁And Q'₂Performing an exclusive OR (XOR) operation to obtain Q₂I.e. by

The step (3-1) comprises the following steps:

(3-1-1) conventional Arnold is transformed by introducing two parameters a and b:

$\left(\begin{array}{c}{x}_{i+1}\\ y_{i+1}\end{array}\right)=\left(\begin{array}{cc}1& 1\\ 1& 2\end{array}\right)\left(\begin{array}{c}{x}_i\\ y_i\end{array}\right)\left(\mathrm{mod}p\right)---\left(3\right)$

expanding to equation (4):

$\left(\begin{array}{c}{x}_{i+1}\\ y_{i+1}\end{array}\right)=\left(\begin{array}{cc}1& a\\ b& ab+1\end{array}\right)\left(\begin{array}{c}{x}_i\\ y_i\end{array}\right)\left(\mathrm{mod}p\right)---\left(4\right)$

(3-1-2) performing two-dimensional Arnold transformation on the formula (4) in an x-y plane while keeping z constant to obtain a formula (5):

$\left(\begin{array}{c}{x}_{i+1}\\ y_{i+1}\\ z_{i+1}\end{array}\right)=\left(\begin{array}{ccc}1& a_z& 0\\ b_z& a_z{b}_z+1& 0\\ 0& 0& 1\end{array}\right)\left(\begin{array}{c}{x}_i\\ y_i\\ z_i\end{array}\right)\left(\mathrm{mod}1\right)---\left(5\right)$

(3-1-3) keeping x unchanged, and performing two-dimensional Arnold transformation on the formula (4) in a y-z plane to obtain a formula (6):

$\left(\begin{array}{c}{x}_{i+1}\\ y_{i+1}\\ z_{i+1}\end{array}\right)=\left(\begin{array}{ccc}1& 0& 0\\ 0& 1& a_x\\ 0& b_x& a_x{b}_x+1\end{array}\right)\left(\begin{array}{c}{x}_i\\ y_i\\ z_i\end{array}\right)\left(\mathrm{mod}1\right)---\left(6\right)$

(3-1-4) performing two-dimensional Arnold transformation on the formula (4) in the x-z plane while keeping y constant to obtain a formula (7):

$\left(\begin{array}{c}{x}_{i+1}\\ y_{i+1}\\ z_{i+1}\end{array}\right)=\left(\begin{array}{ccc}1& 0& a_y\\ 0& 1& 0\\ b_y& 0& a_y{b}_y+1\end{array}\right)\left(\begin{array}{c}{x}_i\\ y_i\\ z_i\end{array}\right)\left(\mathrm{mod}1\right)---\left(7\right)$

(3-1-5) multiplying the coefficient matrixes in the formulas (5), (6) and (7) to obtain a 3D chaotic mapping formula (8):

$\left(\begin{array}{c}{x}_{i+1}\\ y_{i+1}\\ z_{i+1}\end{array}\right)=A\left(\begin{array}{c}{x}_i\\ y_i\\ z_i\end{array}\right)\left(\mathrm{mod}p\right)---\left(8\right)$

wherein,

$A=\left(\begin{array}{ccc}1+a_x{a}_z{a}_y& a_z& a_y+a_x{a}_z+a_x{a}_y{a}_z{b}_x\\ b_z+a_x{b}_y+a_x{a}_z{b}_y{b}_z& a_z{b}_z+1& a_y{a}_z+a_x{a}_y{a}_z{b}_y{b}_z+a_x{a}_z{b}_z+a_x{a}_y{b}_y+a_x\\ a_x{b}_x{b}_y+b_y& b_x& a_x{a}_y{b}_x{b}_y+a_x{b}_x+a_y{b}_y+1\end{array}\right),$

a_xa_ya_zb_xb_yb_zall positive integers.

Matrix a causes the mapping to produce a chaotic effect.

The step (4) comprises the following steps:

and (5) an evolution stage of the cellular automata. Handle Q₂And Q'₂Expanding into two-dimensional plane according to position, and respectively using the two-dimensional plane as two initial states C of 2D second-order cellular automata evolution₀And C₁. According to the rule of step (4-1), C is calculated₀And C₁The Hash value is further used as an initial value and a parameter of the piecewise linear chaotic mapping, so that a random boundary of the cellular automaton is generated. Finally, obtaining a global evolution function G according to the rule number r to enable C_t+1＝G(C_t,C_t-1) And carrying out two evolutions on the two initial states by using the same to obtain C₂And C₃. As shown in fig. 3.

The step (4-1) comprises the following steps:

(4-1-1) setting a two-dimensional cellular automaton with the size of M multiplied by N as C;

(4-1-2) Hash-evaluating C using a 32-bit MD5(Message-Digest Algorithm 5) Algorithm as a Hash function, the value being expressed in 16;

(4-1-3) respectively using 1-16 bits and 17-32 bits of the value to form an initial value x and a parameter p, and obtaining the values of x and p;

(4-1-4) introducing a piecewise linear chaotic mapping definition:

$f\left(x\right)=\left\{\begin{array}{cc}x/p& x\∈\[0,p)\\ (x-p)/(0.5-p)& x\∈\[p,0.5)\\ f(1-x,p)& x\∈\[0.5,1)\end{array}\right.---\left(9\right)$

wherein, the formula (9) is a three-segment linear chaotic system, x belongs to [0,1], p belongs to [0,0.5] is a control parameter of the system;

(4-1-5) operating 2 × (M + N) +4 times using equation (9) to generate random sequences required for all border cells;

(4-1-6) binarizing the sequence results to fill up the supplemented boundary cells in clockwise order from the top left corner of the cellular automaton.

The step (5) comprises the following steps:

and (4) reconstructing the result of the step (4) into a pixel cube, taking the pixel cube as an encryption iteration, and judging whether the iteration number reaches t times. If the iteration number is satisfied, reversely constructing the encrypted image according to the formula (1): otherwise, turning to the step (3), and carrying out the next iteration until the number of times is met.

Example 2

As shown in fig. 4, a basic flow of a confidential method of a digital image encryption method based on a cellular automaton and chaotic mapping is as follows:

(1) a key generation phase;

(2) an image preprocessing stage;

(3) a pixel reverse iteration stage;

(4) a chaotic mapping inverse operation stage;

(5) and (5) circularly executing the steps (3) and (4), judging the iteration frequency condition and outputting the result.

The following steps (1) to (5) are described in detail:

the step (1) comprises the following steps:

a key generation phase. And generating parameters of the 3D chaotic mapping and a rule number of the 2D second-order cellular automata by using the 288-bit binary stream key which is the same as the key in the encryption stage in the same way as in the encryption stage.

The step (2) comprises the following steps:

and (5) an image preprocessing stage. The image is preprocessed in the same way as in the encryption phase, the ciphertext image is blocked, using equation (1):

$W\×H=2N_1^3+2N_2^3+\mathrm{...}+2N_k^3+R---\left(1\right)$

wherein,representing two pixel cubes of equal size, each of length N_kR ∈ (0,1,2, …, 15) is a tail item that cannot be decomposed and is ignored in the subsequent decryption process.

The step (3) comprises the following steps:

and a reverse evolution stage of the cellular automaton. In contrast to the encryption process, the reverse iteration of the cellular automaton is performed on the pixel blocks, and the two initial states of the cellular automaton formed by the ciphertext image blocks are respectively set as C₂And C₃And respectively calculating the Hash values of the two, thereby generating the random boundary of the cellular automaton. Since the inverse rule of the second-order cellular automaton is itself, the reverse global evolution function G' can be obtained according to the rule number r, so that C_t-1＝G′(C_t,C_t+1) After two evolutions, C is obtained₁And C₀As shown in fig. 5.

The step (4) comprises the following steps:

3D chaotic map defined according to equation (2):

$\left(\begin{array}{c}{x}_{i+1}\\ y_{i+1}\\ z_{i+1}\end{array}\right)=A\left(\begin{array}{c}{x}_i\\ y_i\\ z_i\end{array}\right)\left(\mathrm{mod}N\right)---\left(2\right)$

wherein N is the length of the cube, i belongs to [0, N-1], and x, y and z are the coordinates of a pixel in a three-dimensional space respectively.

For the inverse operation, the inverse matrix A of the matrix A needs to be calculated^-1Since det (a) is 1, the inverse matrix is obtainable, 3The inverse mapping definition of the D chaotic map is described by equation (3):

$\left(\begin{array}{c}{x}_i\\ y_i\\ z_i\end{array}\right)=A^{-1}\left(\begin{array}{c}{x}_{i+1}\\ y_{i+1}\\ z_{i+1}\end{array}\right)\left(\mathrm{mod}N\right)---\left(2\right)$

wherein N is the length of the cube, and i belongs to [0, N-1 ].

And (4) respectively and alternately performing exclusive OR (XOR) operation and inverse operation of 3D chaotic mapping (opposite to the encryption process) on the pixel blocks obtained by decryption in the step (3).

The step (5) comprises the following steps:

and (4) circularly executing the steps (3) and (4) until the iteration times t defined in the secret key are met, thereby completing the whole decryption process, and finally reconstructing a plaintext image according to the inverse operation of the formula (1) and completing the decryption.

The same or similar reference numerals correspond to the same or similar parts;

the positional relationships depicted in the drawings are for illustrative purposes only and are not to be construed as limiting the present patent;

it should be understood that the above-described embodiments of the present invention are merely examples for clearly illustrating the present invention, and are not intended to limit the embodiments of the present invention. Other variations and modifications will be apparent to persons skilled in the art in light of the above description. And are neither required nor exhaustive of all embodiments. Any modification, equivalent replacement, and improvement made within the spirit and principle of the present invention should be included in the protection scope of the claims of the present invention.

Claims (6)

1. A digital image encryption method based on cellular automata and chaotic mapping is characterized by comprising the following steps:

s1: generating a key to generate a coefficient, iteration times and an evolution rule of a cellular automaton of the 3D chaotic mapping;

s2: preprocessing an image to be encrypted;

s3: pixel position scrambling is carried out on the pixels of the preprocessed image by using the coefficient of the 3D chaotic mapping obtained in the S1;

s4: and (4) carrying out iterative encryption on the plaintext block of the image after the pixel scrambling by using the cellular automata evolution rule obtained in the S1, repeating iteration until the iteration requirement is met, and finally carrying out reverse preprocessing to obtain the ciphertext image.

2. The digital image encryption method based on cellular automata and chaotic mapping according to claim 1, wherein the specific process of step S1 is as follows:

selecting a 288-bit binary bit stream as a key to generate the coefficients of the 3D chaotic mapping, the iteration times and the rule numbers of the evolution rules of the cellular automata, wherein the key generation algorithm is that the first 7 × 32 bits represent an integer for each 32 bits, and the integers are respectively used as six coefficients of the 3D chaotic mapping (a)_xa_ya_zb_xb_yb_z) And the iteration number t, and the last 64 bits form the rule number r of the cellular automaton.

3. The digital image encryption method based on cellular automata and chaotic map according to claim 2, wherein the specific process of step S2 is as follows:

the pixels of the gray-scale image to be encrypted, which are plain text, are rendered three-dimensional, with the length and height of the image M being W and H, respectively, and the decomposition can be performed according to the following equation:

$W\×H=2N_1^3+2N_2^3+\mathrm{...}+2N_k^3+R---\left(1\right)$

wherein,representing two pixel cubes of equal size, each of length N_kR ∈ (0,1,2, …, 15) is a tail item that cannot be decomposed and is ignored in the subsequent encryption process.

4. The digital image encryption method based on cellular automata and chaotic map according to claim 3, wherein the specific process of step S3 is as follows:

s31: establishing a 3D chaotic mapping function:

1) the conventional Arnold transform is transformed by introducing two parameters a and b:

$\left(\begin{array}{c}{x}_{i+1}\\ y_{i+1}\end{array}\right)=\left(\begin{array}{cc}1& 1\\ 1& 2\end{array}\right)\left(\begin{array}{c}{x}_i\\ y_i\end{array}\right)\left(\mathrm{mod}p\right)---\left(3\right)$

expanding to equation (4):

$\left(\begin{array}{c}{x}_{i+1}\\ y_{i+1}\end{array}\right)=\left(\begin{array}{cc}1& a\\ b& ab+1\end{array}\right)\left(\begin{array}{c}{x}_i\\ y_i\end{array}\right)\left(\mathrm{mod}p\right)---\left(4\right)$

2) keeping z unchanged, and performing two-dimensional Arnold transformation on the formula (4) in an x-y plane to obtain a formula (5):

$\left(\begin{array}{c}{x}_{i+1}\\ y_{i+1}\\ z_{i+1}\end{array}\right)=\left(\begin{array}{ccc}1& a_z& 0\\ b_z& a_z{b}_z+1& 0\\ 0& 0& 1\end{array}\right)\left(\begin{array}{c}{x}_i\\ y_i\\ z_i\end{array}\right)\left(\mathrm{mod}1\right)---\left(5\right)$

3) keeping x unchanged, and performing two-dimensional Arnold transformation on the formula (4) in a y-z plane to obtain a formula (6):

$\left(\begin{array}{c}{x}_{i+1}\\ y_{i+1}\\ z_{i+1}\end{array}\right)=\left(\begin{array}{ccc}1& 0& 0\\ 0& 1& a_x\\ 0& b_x& a_x{b}_x+1\end{array}\right)\left(\begin{array}{c}{x}_i\\ y_i\\ z_i\end{array}\right)\left(\mathrm{mod}1\right)---\left(6\right)$

4) keeping y unchanged, and performing two-dimensional Arnold transformation on the formula (4) in an x-z plane to obtain a formula (7):

$\left(\begin{array}{c}{x}_{i+1}\\ y_{i+1}\\ z_{i+1}\end{array}\right)=\left(\begin{array}{ccc}1& 0& a_y\\ 0& 1& 0\\ b_y& 0& a_y{b}_y+1\end{array}\right)\left(\begin{array}{c}{x}_i\\ y_i\\ z_i\end{array}\right)\left(\mathrm{mod}1\right)---\left(7\right)$

5) multiplying the coefficient matrixes in the formulas (5), (6) and (7) to obtain a 3D chaotic mapping formula (8):

$\left(\begin{array}{c}{x}_{i+1}\\ y_{i+1}\\ z_{i+1}\end{array}\right)=A\left(\begin{array}{c}{x}_i\\ y_i\\ z_i\end{array}\right)\left(\mathrm{mod}p\right)---\left(8\right)$

wherein,

$A=\left(\begin{array}{ccc}1+a_x{a}_z{a}_y& a_z& a_y+a_x{a}_z+a_x{a}_y{a}_z{b}_x\\ b_z+a_x{b}_y+a_x{a}_z{b}_y{b}_z& a_z{b}_z+1& a_y{a}_z+a_x{a}_y{a}_z{b}_y{b}_z+a_x{a}_z{b}_z+a_x{a}_y{b}_y+a_x\\ a_x{b}_x{b}_y+b_y& b_x& a_x{a}_y{b}_x{b}_y+a_x{b}_x+a_y{b}_y+1\end{array}\right),$

a_xa_ya_zb_xb_yb_zall are positive integers, N is the length of the cube, i ∈ [0, N-1]X, y and z are coordinates of a pixel in a three-dimensional space respectively;

s32: and performing position scrambling processing on the pixels by using the obtained 3D chaotic mapping function:

firstly, carrying out 3D chaotic mapping on Q once by using a formula (2) to obtain Q₁Then Q is₁And Q' is exclusive-OR (XOR) at each position to obtain QThen to Q'₁Performing 3D chaotic mapping to obtain Q'₂And finally Q₁And Q'₂Performing an exclusive OR (XOR) operation to obtain Q₂I.e. byWhere Q and Q' characterize a pair of pixel cubes of equal volume for the image.

5. The digital image encryption method based on cellular automata and chaotic map according to claim 4, wherein the specific process of step S4 is as follows:

handle Q₂And Q'₂Expanding into two-dimensional plane according to position, and respectively using the two-dimensional plane as two initial states C of 2D second-order cellular automata evolution₀And C₁Calculating C₀And C₁The Hash value is used as an initial value and a parameter of piecewise linear chaotic mapping so as to generate a random boundary of the cellular automaton, and a global evolution function G is obtained according to a rule number r so that C is obtained_t+1＝G(C_t,C_t-1) And carrying out two evolutions on the two initial states by using the same to obtain C₂And C₃Mixing C with₂And C₃Reconstructing a pixel cube, taking the cube as a primary encryption iteration, judging whether the iteration number reaches t times, if so, reversely constructing an encrypted image according to a formula (1): otherwise, go to step S3 to perform the next iteration until the number of times is satisfied.

6. A decryption method for the digital image encryption method based on cellular automata and chaotic mapping according to claim 5, comprising the steps of:

s61: generating parameters of 3D chaotic mapping and rule numbers of a 2D second-order cellular automaton by using the 288-bit binary stream key which is the same as that in the encryption stage in the same way;

s62: preprocessing the image to be decrypted in the same way as the encryption stage;

s63: performing reverse iteration of the cellular automaton on the pixel blocks, and setting two initial states of the cellular automaton formed by the ciphertext image blocks as C₂And C₃Respectively calculating the Hash values of the two, thereby generating a random boundary of the cellular automata, and obtaining a reverse global evolution function G' according to a rule number r because an inverse rule of the second-order cellular automata is the random boundary of the second-order cellular automata, so that C_t-1＝G′(C_t,C_t+1) After two evolutions, C is obtained₁And C₀；

S64: establishing an inverse mapping function of the 3D chaotic mapping:

$\left(\begin{array}{c}{x}_i\\ y_i\\ z_i\end{array}\right)=A^{-1}\left(\begin{array}{c}{x}_{i+1}\\ y_{i+1}\\ z_{i+1}\end{array}\right)\left(\mathrm{mod}N\right)$

wherein A is^-1Is the inverse matrix of A, N is the length of the cube, i ∈ [0, N-1]X, y and z are coordinates of a pixel in a three-dimensional space respectively, and the pixel blocks obtained by decryption in S63 are subjected to cross exclusive OR (XOR) operation and inverse operation of 3D chaotic mapping respectively;

s65: and (3) circularly executing the steps S63 and S64 until the iteration number t defined in the key is met, thereby completing the whole decryption process, and finally reconstructing the plaintext image according to the inverse operation of the formula (1) and completing the decryption.